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diff --git a/linguistics/semantics.md b/linguistics/semantics.md index 105a0fd..96bbb17 100644 --- a/linguistics/semantics.md +++ b/linguistics/semantics.md @@ -23,16 +23,20 @@ This framework is [first-order/predicate logic](../mathematics/logic) and the [s ### Predicate Logic & The Lambda Calculus -Formal semantics begets a formal system for such semantics, and *first-order logic* and *the lambda calculus* are a natural fit. As discussed above, language functions by composition - and what are functions but their property of composition? +Formal semantics begets a formal system for such semantics, and *first-order logic* and *the lambda calculus* are a natural fit. Semantics is the study of meaning - and what is logic but a system for expressing meaning? As discussed above, language functions by composition - and what are functions but their property of composition? -[*An Invitation to Formal Semantics*](https://eecoppock.info/bootcamp/semantics-boot-camp.pdf) covers basic logic and the lambda calculus well in its first six chapters. Otherwise, see [logic](../mathematics/logic), and [lambda-calculus](../plt/lambda-calculus). +[*An Invitation to Formal Semantics*](https://eecoppock.info/bootcamp/semantics-boot-camp.pdf) covers basic logic and the lambda calculus well in its first six chapters. Otherwise, for a worse introduction, see [logic](../mathematics/logic), and [the lambda calculus](../plt/lambda-calculus). ## Denotational Semantics -With basic logic and the lambda calculus as our base, we may simply get straight to assigning *meaning* to language. +With basic logic and the lambda calculus under our belt, we may simply get straight to assigning *meaning* to language. We consider two *basic types* to start: the type of entities, $e$, and the type of truth values, $t$. Our function types we denote by ordered pairs: that is, a function from $e$ to $t$ is of type $⟨e,t⟩$. This is perhaps clunkier notation than the type-theoretic $e→t$, but it is what it is. (And does avoid issues of precedence.) ### Entities and Functions +> I am Alice. +> Alice is bad. +> The blue pigeon flew away. + ### Quantification ### Reference @@ -49,6 +53,10 @@ With basic logic and the lambda calculus as our base, we may simply get straight ### Command, Request, Obligation +> Alice, run!<br> +> Alice, please run.<br> +> Alice should run. + ### Questions ## Resources - ✨ [Invitation to Formal Semantics](https://eecoppock.info/bootcamp/semantics-boot-camp.pdf) |